
import pandas as pd
import plotly.express as px
import seaborn as sns
import numpy as np
import matplotlib.pyplot as plt

from statsmodels.tsa.stattools import adfuller
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
from statsmodels.tsa.arima.model import ARIMA
from statsmodels.tsa.seasonal import seasonal_decompose
import statsmodels.api as sm

from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_absolute_error, mean_absolute_percentage_error, mean_squared_error
from sklearn.model_selection import train_test_split
from sklearn.metrics import r2_score

import pmdarima as pm

from prophet import Prophet
from prophet.plot import plot_plotly, plot_components_plotly
from prophet.plot import add_changepoints_to_plot

D:\Anaconda\envs\env_fisica\lib\site-packages\statsmodels\tsa\base\tsa_model.py:7: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import (to_datetime, Int64Index, DatetimeIndex, Period,
D:\Anaconda\envs\env_fisica\lib\site-packages\statsmodels\tsa\base\tsa_model.py:7: FutureWarning: pandas.Float64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import (to_datetime, Int64Index, DatetimeIndex, Period,


df_original = pd.read_csv("data/globaltemperatures.csv")
df = df_original.copy(deep=True)
df.head()


# feature LandAverageTemperature

fig = px.line(df, x=df.dt, y="LandAverageTemperature", title='Livello mensile')
fig.show()

# si osserva un trend leggermente crescente negli ultimi anni in particolare


# feature LandAverageTemperatureUncertainty

fig = px.line(df, x=df.dt, y="LandAverageTemperatureUncertainty", title='Livello mensile')
fig.show()

# come prevedibile andando nel passato l'incertezza sui valori di LandAverageTemperature cresce


df.shape

(3192, 3)


df.dtypes

dt                                    object
LandAverageTemperature               float64
LandAverageTemperatureUncertainty    float64
dtype: object


df.describe(include='all')


sum(df.duplicated())

# non ci sono duplicati

0


df.isna().sum()

# sono presenti alcuni valori mancanti

dt                                    0
LandAverageTemperature               12
LandAverageTemperatureUncertainty    12
dtype: int64


# vengono analizzati nel dettaglio i valori mancanti

df[df.isna().any(axis=1)]

# dunque i valori mancanti si riferiscono ai primi anni della serie storica


# interpolate: Fill NaN values using an interpolation method
# method ‘time’: Works on daily and higher resolution data to interpolate given length of interval
df = df.interpolate(option='time')

# verifica grafico bontà correzione
fig = px.line(df, x=df.dt, y="LandAverageTemperature", title='Livello mensile')
fig.show()


# sistemazione del formato feature data ('dt')

df['dt'] = pd.to_datetime(df['dt'], format='%Y/%m/%d')
df


# aggiunta di altre feature potenzialmente utili

df['month'] = df['dt'].dt.month
df['year'] = df['dt'].dt.year
df


# la feature dt viene impostata come indice del dataframe

df.set_index('dt', inplace=True)


df.head()


# livello mensile senza missing values

fig = px.line(df, x=df.index, y="LandAverageTemperature", title='Livello mensile')
fig.show()


# grafico a specchio a livello mensile

plt.figure(figsize=(16,5))
plt.fill_between(df.index, y1=df['LandAverageTemperature'], y2=-df['LandAverageTemperature'], alpha=0.5, linewidth=2, color='blue')
plt.hlines(y=0, xmin=np.min(df.index), xmax=np.max(df.index), linewidth=.5)
plt.show()


# livello annuale

df_year = df[['LandAverageTemperature']].resample("Y").sum()
fig = px.line(df_year, x=df_year.index, y="LandAverageTemperature", title='Livello annuale')
fig.show()


# a livello mensile

fig, ax = plt.subplots(figsize=(20, 6))

sns.boxplot(df['month'], df['LandAverageTemperature'])
ax.set_xlabel('month')
ax.set_ylabel('LandAverageTemperature')

plt.show()

# si nota già qui una stagionalità mensile (ripetizioni di pattern simili ogni 12 osservazioni, ovvero ogni anno), ovvero un aumento delle temperatura terrestre media nei mesi centrali dell'anno

D:\Anaconda\envs\env_fisica\lib\site-packages\seaborn\_decorators.py:36: FutureWarning:

Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.


fig, axes = plt.subplots(1, 2, figsize=(20,6))
plot_acf(df.LandAverageTemperature.tolist(), lags=25, ax=axes[0])
plot_pacf(df.LandAverageTemperature.tolist(), lags=25, ax=axes[1])
plt.show()

# si può notare la presenza di stagionalità come già osservato in precedenza


df_test = df.ffill()

result_add = seasonal_decompose(df_test['LandAverageTemperature'], model='additive', extrapolate_trend='freq')

# plot
plt.rcParams.update({'figure.figsize': (16, 9)})
result_add.plot()
plt.show()


plt.figure(figsize=(16,5))
result_add.trend.plot(legend=False)

# viene rappresentata la pendenza positiva osservata nei dati

# si può osservare un chiaro trend positivo il che indicherebbe che le temperature sono in aumento, in particolar modo negli ultimi anni. Nei primi anni a disposizione si registra una maggiore variabilità

<AxesSubplot:xlabel='dt'>


result_add.trend

dt
1750-01-01    8.387605
1750-02-01    8.360928
1750-03-01    8.334252
1750-04-01    8.307576
1750-05-01    8.280900
                ...   
2015-08-01    9.766115
2015-09-01    9.777700
2015-10-01    9.789285
2015-11-01    9.800871
2015-12-01    9.812456
Name: trend, Length: 3192, dtype: float64


plt.figure(figsize=(16,5))
result_add.seasonal.plot(legend=False)

# si osserva una forte stagionalità che verrà analizzata più nel dettaglio a seguire

<AxesSubplot:xlabel='dt'>


result_add.seasonal

dt
1750-01-01   -6.093454
1750-02-01   -5.406483
1750-03-01   -3.411714
1750-04-01   -0.120741
1750-05-01    2.769936
                ...   
2015-08-01    5.365940
2015-09-01    3.335971
2015-10-01    0.508751
2015-11-01   -2.636375
2015-12-01   -5.175941
Name: seasonal, Length: 3192, dtype: float64


# si analizza più nel dettaglio la stagionalità considerando una finestra temporale ridotta

seasonal_decompose(df_test['LandAverageTemperature'][100:243], model='additive', extrapolate_trend='freq').seasonal.plot(legend=False)

# anche in questo caso si osserva un picco negativo all'inizio dell'anno (temperature basse nei mesi invernali) e un picco positivo (temperature alte nei mesi estivi). Questo pattern si ripete nel corso degli anni

<AxesSubplot:xlabel='dt'>


cycle, trend = sm.tsa.filters.hpfilter(df.LandAverageTemperature, 129600)
decomp = df[['LandAverageTemperature']]
decomp["cycle"] = cycle
decomp["trend"] = trend

fig, ax = plt.subplots()
decomp[["LandAverageTemperature", "trend", "cycle"]].plot(ax=ax, figsize=(12, 5))
plt.show()

C:\Users\loren\AppData\Local\Temp\ipykernel_1212\1096149108.py:3: SettingWithCopyWarning:


A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy

C:\Users\loren\AppData\Local\Temp\ipykernel_1212\1096149108.py:4: SettingWithCopyWarning:


A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy


rolmean = df[['LandAverageTemperature']].rolling(window=12).mean() #window size 12 denotes 12 months, giving rolling mean at yearly level
rolstd = df[['LandAverageTemperature']].rolling(window=12).std()

#Plot rolling statistics
orig = plt.plot(df[['LandAverageTemperature']], color='blue', label='Original')
mean = plt.plot(rolmean, color='red', label='Rolling Mean')
std = plt.plot(rolstd, color='black', label='Rolling Std')
plt.legend(loc='best')
plt.title('Rolling Mean & Standard Deviation')
plt.show(block=False)

# per soddisfare la condizione di stazionarietà della serie è bene che la rolling mean e la rolling standard deviation rimangano invarianti/costanti nel tempo. Dunque le due curve dovrebbero essere parallele
# all'asse x e in questo caso tale condizione è in parte soddisfatta


trend_df = pd.DataFrame()
trend_df['y'] = result_add.trend
trend_df = trend_df.reset_index()
trend_df['x'] = list(range(1,3193,1))
trend_df = trend_df[['x', 'y']]
trend_df


X_train, X_test, Y_train, Y_test = train_test_split(trend_df[['x']], trend_df[['y']], test_size=0.3, random_state=0)


regr = LinearRegression()
regr.fit(X_train, Y_train)

LinearRegression()


Y_pred_train = regr.predict(X_train) # si esegue la predizione sul train set
Y_pred_test = regr.predict(X_test) # si esegue la predizione anche sul test set


# i valori variano da 0 a inf
# sono da preferire valori piccoli

print("MAE train: %f" % mean_absolute_error(Y_train, Y_pred_train))
print("MAE test: %f" % mean_absolute_error(Y_test, Y_pred_test))

MAE train: 0.327771
MAE test: 0.345392


# l'MSE da un peso maggiore agli errori più grandi

print("MSE train: %f" % mean_squared_error(Y_train, Y_pred_train))
print("MSE test: %f" % mean_squared_error(Y_test, Y_pred_test))

MSE train: 0.193238
MSE test: 0.203991


# si riporta il valore di R2 i cui valori variano da -inf a +1
# R2 riporta l'errore del modello in termini percentuali
# valori elevati sono da preferire

print("R2 train: %f" % r2_score(Y_train, Y_pred_train))
print("R2 test: %f" % r2_score(Y_test, Y_pred_test))

R2 train: 0.388888
R2 test: 0.418816


model = LinearRegression()


x = trend_df['x'].values
y = trend_df['y'].values


x = x.reshape(3192, 1)
y = y.reshape(3192, 1)


model = model.fit(x, y)


y_p = model.predict(x)

print("MAE: %f" % mean_absolute_error(y, y_p))
print("MSE: %f" % mean_squared_error(y, y_p))
print("R2: %f" % r2_score(y, y_p))

MAE: 0.333539
MSE: 0.196355
R2: 0.398927


plt.scatter(x, y, color='black')
plt.plot(x, y_p, color='blue', linewidth=3)
plt.xticks(())
plt.yticks(())
plt.show()

# come osservato in precedenza la tendenza del trend è positiva, in crescita


df_arima = df[['LandAverageTemperature']]
df_arima


result = adfuller(df_arima.LandAverageTemperature)

print('ADF Statistic: %f' % result[0])
print('p-value: %f' % result[1])
print('Critical Values:')

for key, value in result[4].items():
    print('\t%s: %.3f' % (key, value))

# il test sembra indicare che la serie sia stazionaria

ADF Statistic: -4.036404
p-value: 0.001231
Critical Values:
	1%: -3.432
	5%: -2.862
	10%: -2.567


# per completezza si prova ad eliminare trend e stagionalità


# viene rimosso il trend

plt.rcParams.update({'figure.figsize': (10, 5)})

df_detrend = df_arima.copy()
plt.plot(df_detrend.index, df_detrend.LandAverageTemperature)
plt.show()

result_mul = seasonal_decompose(df_detrend['LandAverageTemperature'], model='additive', extrapolate_trend='freq')
detrended = df_detrend.LandAverageTemperature.values - result_mul.trend

plt.plot(df_detrend.index, detrended)
plt.show()


# viene rimossa la stagionalità

plt.rcParams.update({'figure.figsize': (10, 5)})

df_deseason = df_arima.copy()
plt.plot(df_deseason.index, df_deseason.LandAverageTemperature)
plt.show()

result_mul = seasonal_decompose(df_deseason['LandAverageTemperature'], model='additive', extrapolate_trend='freq')
deseasonalized = df_deseason.LandAverageTemperature.values / result_mul.seasonal

plt.plot(df_deseason.index, deseasonalized)
plt.show()


# si procede tuttavia supponendo che i dati siano stazionari


df_train = df_arima[df_arima.index < '2005-02-01'].copy()['LandAverageTemperature']

df_test = df_arima[df_arima.index >= '2005-02-01'].copy()['LandAverageTemperature']

# check sample size
print('Train: ', df_train.size)
print('Test: ', df_test.size)

Train:  3061
Test:  131


# il metodo auto_arima permette di determinare automaticamente la migliore combinazione dei valori p, q e d necessari alla costruzione del modello

smodel = pm.auto_arima(df_arima, start_p=1, start_q=1,
                       test='adf',
                       max_p=3, max_q=3, m=12,
                       start_P=0, seasonal=True,
                       d=None, D=1, trace=True,
                       error_action='ignore',
                       suppress_warnings=True,
                       stepwise=True)

smodel.summary()

Performing stepwise search to minimize aic
 ARIMA(1,0,1)(0,1,1)[12] intercept   : AIC=inf, Time=5.79 sec
 ARIMA(0,0,0)(0,1,0)[12] intercept   : AIC=9612.931, Time=0.13 sec
 ARIMA(1,0,0)(1,1,0)[12] intercept   : AIC=8397.982, Time=1.42 sec
 ARIMA(0,0,1)(0,1,1)[12] intercept   : AIC=inf, Time=2.63 sec
 ARIMA(0,0,0)(0,1,0)[12]             : AIC=9611.011, Time=0.11 sec
 ARIMA(1,0,0)(0,1,0)[12] intercept   : AIC=9230.828, Time=0.34 sec
 ARIMA(1,0,0)(2,1,0)[12] intercept   : AIC=8150.327, Time=3.79 sec
 ARIMA(1,0,0)(2,1,1)[12] intercept   : AIC=inf, Time=12.47 sec
 ARIMA(1,0,0)(1,1,1)[12] intercept   : AIC=inf, Time=3.46 sec
 ARIMA(0,0,0)(2,1,0)[12] intercept   : AIC=8568.081, Time=2.42 sec
 ARIMA(2,0,0)(2,1,0)[12] intercept   : AIC=8145.469, Time=3.76 sec
 ARIMA(2,0,0)(1,1,0)[12] intercept   : AIC=8394.395, Time=1.77 sec
 ARIMA(2,0,0)(2,1,1)[12] intercept   : AIC=inf, Time=21.29 sec
 ARIMA(2,0,0)(1,1,1)[12] intercept   : AIC=inf, Time=10.15 sec
 ARIMA(3,0,0)(2,1,0)[12] intercept   : AIC=8144.106, Time=5.86 sec
 ARIMA(3,0,0)(1,1,0)[12] intercept   : AIC=8390.472, Time=2.29 sec
 ARIMA(3,0,0)(2,1,1)[12] intercept   : AIC=inf, Time=28.67 sec
 ARIMA(3,0,0)(1,1,1)[12] intercept   : AIC=inf, Time=14.49 sec
 ARIMA(3,0,1)(2,1,0)[12] intercept   : AIC=8141.277, Time=14.52 sec
 ARIMA(3,0,1)(1,1,0)[12] intercept   : AIC=8383.882, Time=5.83 sec
 ARIMA(3,0,1)(2,1,1)[12] intercept   : AIC=inf, Time=31.13 sec
 ARIMA(3,0,1)(1,1,1)[12] intercept   : AIC=inf, Time=10.45 sec
 ARIMA(2,0,1)(2,1,0)[12] intercept   : AIC=8146.407, Time=10.13 sec
 ARIMA(3,0,2)(2,1,0)[12] intercept   : AIC=8127.091, Time=20.67 sec
 ARIMA(3,0,2)(1,1,0)[12] intercept   : AIC=inf, Time=13.86 sec
 ARIMA(3,0,2)(2,1,1)[12] intercept   : AIC=inf, Time=32.00 sec
 ARIMA(3,0,2)(1,1,1)[12] intercept   : AIC=inf, Time=13.66 sec
 ARIMA(2,0,2)(2,1,0)[12] intercept   : AIC=8135.489, Time=16.31 sec
 ARIMA(3,0,3)(2,1,0)[12] intercept   : AIC=inf, Time=36.83 sec
 ARIMA(2,0,3)(2,1,0)[12] intercept   : AIC=8129.397, Time=15.67 sec
 ARIMA(3,0,2)(2,1,0)[12]             : AIC=8125.363, Time=8.58 sec
 ARIMA(3,0,2)(1,1,0)[12]             : AIC=inf, Time=6.72 sec
 ARIMA(3,0,2)(2,1,1)[12]             : AIC=inf, Time=25.27 sec
 ARIMA(3,0,2)(1,1,1)[12]             : AIC=inf, Time=11.69 sec
 ARIMA(2,0,2)(2,1,0)[12]             : AIC=8133.778, Time=4.38 sec
 ARIMA(3,0,1)(2,1,0)[12]             : AIC=8139.557, Time=4.30 sec
 ARIMA(3,0,3)(2,1,0)[12]             : AIC=inf, Time=14.09 sec
 ARIMA(2,0,1)(2,1,0)[12]             : AIC=8144.645, Time=3.33 sec
 ARIMA(2,0,3)(2,1,0)[12]             : AIC=8127.683, Time=4.41 sec

Best model:  ARIMA(3,0,2)(2,1,0)[12]          
Total fit time: 424.699 seconds


# il modello migliore ottenuto risulta essere:
# ARIMA(order=(3, 0, 2), scoring_args={}, seasonal_order=(2, 1, 0, 12), suppress_warnings=True, with_intercept=False)

model_arima = ARIMA(df_train,
             order=(3, 0, 2),
             seasonal_order=(2, 1, 0, 12))
model_arima = model_arima.fit()

D:\Anaconda\envs\env_fisica\lib\site-packages\statsmodels\tsa\base\tsa_model.py:524: ValueWarning:

No frequency information was provided, so inferred frequency MS will be used.

D:\Anaconda\envs\env_fisica\lib\site-packages\statsmodels\tsa\base\tsa_model.py:524: ValueWarning:

No frequency information was provided, so inferred frequency MS will be used.

D:\Anaconda\envs\env_fisica\lib\site-packages\statsmodels\tsa\base\tsa_model.py:524: ValueWarning:

No frequency information was provided, so inferred frequency MS will be used.


# analisi acf e pacf dei redsidui del modello migliore

plot_acf(model_arima.resid)


# previsioni sul test set

pred = model_arima.get_prediction(start=df_test.index[0], end=df_test.index[-1]).predicted_mean
pred

D:\Anaconda\envs\env_fisica\lib\site-packages\statsmodels\tsa\base\tsa_model.py:132: FutureWarning:

The 'freq' argument in Timestamp is deprecated and will be removed in a future version.

2005-02-01     4.385457
2005-03-01     6.306328
2005-04-01     9.181811
2005-05-01    11.943538
2005-06-01    14.005319
                ...    
2015-08-01    14.408232
2015-09-01    12.770561
2015-10-01    10.195165
2015-11-01     7.060713
2015-12-01     4.502828
Freq: MS, Name: predicted_mean, Length: 131, dtype: float64


fig=plt.figure(figsize=(20,8), dpi=80)
fig.show()
ax=fig.add_subplot()
plt.title('Prediction with ARIMA')
plt.xlabel('Date')
plt.ylabel('CO')
ax.plot(df_test, label='Actual')
ax.plot(pred, label='Prediction')
plt.legend()
plt.show()

C:\Users\loren\AppData\Local\Temp\ipykernel_1212\1530992414.py:2: UserWarning:

Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.


# performances sul test set

aic = model_arima.aic
mape = mean_absolute_percentage_error(df_test, pred)
print('AIC: ', int(aic))
print('MAPE:', round(mape, 4))

AIC:  7902
MAPE: 0.0441


dates_future = pd.date_range(start='2016-01-01', end='2026-01-01', freq='M')
df_future = pd.DataFrame()
df_future.index = dates_future
df_future['LandAverageTemperature'] = None
df_future


# previsioni dal 2016 al 2026

pred = model_arima.get_prediction(start=df_future.index[0], end=df_future.index[-1]).predicted_mean
pred

D:\Anaconda\envs\env_fisica\lib\site-packages\statsmodels\tsa\base\tsa_model.py:132: FutureWarning:

The 'freq' argument in Timestamp is deprecated and will be removed in a future version.

2016-02-01     4.381133
2016-03-01     6.275381
2016-04-01     9.199070
2016-05-01    11.853855
2016-06-01    13.968382
                ...    
2025-09-01    12.770596
2025-10-01    10.195111
2025-11-01     7.060663
2025-12-01     4.502734
2026-01-01     3.745296
Freq: MS, Name: predicted_mean, Length: 120, dtype: float64


plt.figure(figsize=(20, 8), dpi=80)
plt.plot(df_arima['LandAverageTemperature'])
plt.plot(pred)
plt.show()


df_prophet = df_arima.copy(deep=True)
df_prophet

# con Prophet non è necessario rendere stazionaria la serie


df_prophet = df_prophet.reset_index()
df_prophet


df_prophet = df_prophet.rename(columns = {'dt': 'ds', 'LandAverageTemperature':'y'})
df_prophet


df_prophet_train = df_prophet[df_prophet.ds < '2005-02-01'].copy()

df_prophet_test = df_prophet[df_prophet.ds >= '2005-02-01'].copy()

# check sample size
print('Train: ', df_prophet_train.size)
print('Test: ', df_prophet_test.size)

Train:  6122
Test:  262


model_prophet = Prophet()
model_prophet.fit(df_prophet_train)

INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.
INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.
D:\Anaconda\envs\env_fisica\lib\site-packages\prophet\forecaster.py:896: FutureWarning:

The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.

<prophet.forecaster.Prophet at 0x257a7fe0e50>


future = model_prophet.make_future_dataframe(periods=132, freq='M')
future


forecast = model_prophet.predict(future)
forecast[['ds', 'yhat', 'yhat_lower', 'yhat_upper']].tail()
forecast_values = forecast[forecast.ds >= '2005-02-01'].copy()
forecast_values = forecast_values.reset_index()

D:\Anaconda\envs\env_fisica\lib\site-packages\prophet\forecaster.py:896: FutureWarning:

The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.

D:\Anaconda\envs\env_fisica\lib\site-packages\prophet\forecaster.py:896: FutureWarning:

The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.


ax=forecast_values.plot(x='ds',y='yhat',legend=True,label='predictions',figsize=(40,8))
df_prophet_test.plot(x='ds',y='y',legend=True,label='True Test Data',ax=ax)

<AxesSubplot:xlabel='ds'>


df_merge = pd.DataFrame()
df_prophet_test = df_prophet_test.reset_index()
df_merge['true'] = df_prophet_test['y']
df_merge['predicted'] = forecast_values['yhat']
df_merge


y_true = df_merge['true'].values
y_pred = df_merge['predicted'].values
mae = mean_absolute_error(y_true, y_pred)
mape = mean_absolute_percentage_error(y_true, y_pred)
mape*100

# si ottiene un risultato migliore con il modello ARIMA in termini di MAPE

24.245989876591377


model_prophet = Prophet()
model_prophet.fit(df_prophet)

INFO:prophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.
INFO:prophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.
D:\Anaconda\envs\env_fisica\lib\site-packages\prophet\forecaster.py:896: FutureWarning:

The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.

<prophet.forecaster.Prophet at 0x257df1c8af0>


future = model_prophet.make_future_dataframe(periods=120, freq='M')


forecast = model_prophet.predict(future)
forecast[['ds', 'yhat', 'yhat_lower', 'yhat_upper']].tail()

D:\Anaconda\envs\env_fisica\lib\site-packages\prophet\forecaster.py:896: FutureWarning:

The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.

D:\Anaconda\envs\env_fisica\lib\site-packages\prophet\forecaster.py:896: FutureWarning:

The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.


model_prophet.plot(forecast)


plot_plotly(model_prophet, forecast)


plot_components_plotly(model_prophet, forecast)

D:\Anaconda\envs\env_fisica\lib\site-packages\prophet\forecaster.py:896: FutureWarning:

The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.


fig = model_prophet.plot(forecast)
a = add_changepoints_to_plot(fig.gca(), model_prophet, forecast)

	dt	LandAverageTemperature	LandAverageTemperatureUncertainty
0	1750-01-01	3.034	3.574
1	1750-02-01	3.083	3.702
2	1750-03-01	5.626	3.076
3	1750-04-01	8.490	2.451
4	1750-05-01	11.573	2.072

	dt	LandAverageTemperature	LandAverageTemperatureUncertainty
0	1750-01-01	3.034	3.574
1	1750-02-01	3.083	3.702
2	1750-03-01	5.626	3.076
3	1750-04-01	8.490	2.451
4	1750-05-01	11.573	2.072
...	...	...	...
3187	2015-08-01	14.755	0.072
3188	2015-09-01	12.999	0.079
3189	2015-10-01	10.801	0.102
3190	2015-11-01	7.433	0.119
3191	2015-12-01	5.518	0.100

Dep. Variable:	y	No. Observations:	3192
Model:	SARIMAX(3, 0, 2)x(2, 1, [], 12)	Log Likelihood	-4054.682
Date:	Tue, 12 Jul 2022	AIC	8125.363
Time:	08:16:36	BIC	8173.880
Sample:	0	HQIC	8142.763
	- 3192
Covariance Type:	opg

	coef	std err	z	P>\|z\|	[0.025	0.975]
ar.L1	1.3121	0.059	22.117	0.000	1.196	1.428
ar.L2	-0.9475	0.079	-11.987	0.000	-1.102	-0.793
ar.L3	0.1620	0.027	5.922	0.000	0.108	0.216
ma.L1	-0.9791	0.056	-17.425	0.000	-1.089	-0.869
ma.L2	0.6793	0.056	12.029	0.000	0.569	0.790
ar.S.L12	-0.5969	0.011	-56.747	0.000	-0.618	-0.576
ar.S.L24	-0.2727	0.009	-28.970	0.000	-0.291	-0.254
sigma2	0.7487	0.009	83.298	0.000	0.731	0.766

Ljung-Box (L1) (Q):	0.01	Jarque-Bera (JB):	6547.04
Prob(Q):	0.93	Prob(JB):	0.00
Heteroskedasticity (H):	0.06	Skew:	0.36
Prob(H) (two-sided):	0.00	Kurtosis:	9.99

	dt	LandAverageTemperature	LandAverageTemperatureUncertainty
count	3192	3180.000000	3180.000000
unique	3192	NaN	NaN
top	1750-01-01	NaN	NaN
freq	1	NaN	NaN
mean	NaN	8.374731	0.938468
std	NaN	4.381310	1.096440
min	NaN	-2.080000	0.034000
25%	NaN	4.312000	0.186750
50%	NaN	8.610500	0.392000
75%	NaN	12.548250	1.419250
max	NaN	19.021000	7.880000

	dt	LandAverageTemperature	LandAverageTemperatureUncertainty
10	1750-11-01	NaN	NaN
16	1751-05-01	NaN	NaN
18	1751-07-01	NaN	NaN
21	1751-10-01	NaN	NaN
22	1751-11-01	NaN	NaN
23	1751-12-01	NaN	NaN
25	1752-02-01	NaN	NaN
28	1752-05-01	NaN	NaN
29	1752-06-01	NaN	NaN
30	1752-07-01	NaN	NaN
31	1752-08-01	NaN	NaN
32	1752-09-01	NaN	NaN

	x	y
0	1	8.387605
1	2	8.360928
2	3	8.334252
3	4	8.307576
4	5	8.280900
...	...	...
3187	3188	9.766115
3188	3189	9.777700
3189	3190	9.789285
3190	3191	9.800871
3191	3192	9.812456

	LandAverageTemperature
2016-01-31	None
2016-02-29	None
2016-03-31	None
2016-04-30	None
2016-05-31	None
...	...
2025-08-31	None
2025-09-30	None
2025-10-31	None
2025-11-30	None
2025-12-31	None

	true	predicted
0	3.920	5.880226
1	6.544	8.894414
2	9.618	11.833168
3	12.226	14.112044
4	14.476	15.027346
...	...	...
126	14.755	12.920931
127	12.999	10.449628
128	10.801	6.543147
129	7.433	4.397306
130	5.518	3.239758

	ds	yhat	yhat_lower	yhat_upper
3307	2025-07-31	15.015693	13.993421	16.105879
3308	2025-08-31	13.288761	12.192507	14.352335
3309	2025-09-30	10.748907	9.665598	11.818860
3310	2025-10-31	7.034858	6.006985	8.139212
3311	2025-11-30	4.778510	3.661109	5.824272

Esercizio serie storica¶

Indice¶

Setting ¶

Lettura dataset ¶

Pre processing ed Esplorazione ¶

Caratteristiche principali¶

Verifica duplicati¶

Verifica missing values¶

Gestione missing values¶

Feature engineering¶

Serie storica a diverse granularità¶

Analisi distribuzione variabile di interesse¶

Analisi autocorrelazione¶

Decomposizione¶

Analisi tendenza¶

Analisi stagionalità¶

Trend e Ciclo¶

Rolling Mean e Standard Deviation¶

Regressione lineare del trend ¶

Preparazione dati¶

Divisione in train e test set¶

Fit del modello sul train test¶

Previsioni sul test set¶

Performances sul test set¶

Fit del modello su tutti i dati¶

Previsioni¶

Visualizzazione risultati¶

Previsioni con ARIMA ¶

Preparazione dati¶

Verifica stazionarietà¶

Divisione in train e test¶

Implementazione modello¶

Analisi dei residui modello selezionato¶

Previsioni sul test set¶

Valutazione performances sul test set¶

Previsioni dal 2016 al 2026¶

Previsioni con Prophet ¶

Preparazione dati¶

Divisione in train e test¶

Implementazione modello¶

Previsioni sul test set¶

Valutazione performances sul test set¶

Previsioni dal 2016 al 2026¶